Product Power Property

Presentation

•

Mathematics

•

9th - 12th Grade

•

Hard

Joseph Anderson

FREE Resource

23 Slides • 17 Questions

Product of Powers

Words: when multiplying like bases, add the exponents

Symbols: (x^a)(x^b) = x^a+b

Numbers: (8³)(8⁶) = 8⁹

Product of Power: Product Rule

The product rule states that when multiplying two numbers with the same base, you can add their exponents:

Poll

My level of understanding

(left to right, NO: I don't get it at all, Whoops: need some help but I'm starting to understand, Nailed It: I can do this on my own.

Multiple Choice

(2m³)(3m⁴) =

5m⁷

6m¹²

5m¹²

6m⁷

Power of a Power

Words: when a power (base with exponent) is raised to another power (exponent), you multiply the exponents (keep the base!)

Symbols: (x^a)^b= x^ab

Numbers: (8³)⁶=8¹⁸

Multiple Choice

Simplify:

$\left(2^3\right)^4$

$6^4$

$8^3$

$2^7$

$2^{12}$

Multiple Choice

Simplify

$\left(3a^2c\right)^3$

$9a^6c^3$

$27a^5c^3$

$27a^6c^3$

$9a^5c^3$

Power of a product (Distributive Rule)

Zero Exponent

Fill in the Blanks

Type answer...

Power of a Quotient

Quotient of Powers

Zero Exponent

Power of a Quotient

Quotient of Powers

Power of a Power

Words: when a power (base with exponent) is raised to another power (exponent), you multiply the exponents (keep the base!)

Symbols: (x^a)^b= x^ab

Numbers: (8³)⁶=8¹⁸

Power of a Product

Zero Exponent

Power of a Quotient

Quotient of Powers

Multiple Choice

Simplify:

$\frac{5^7}{5^4}$

$5^{11}$

$1^3$

$5^3$

Power of a Product

Power of a Product: Example

Multiple Choice

Now it's your turn. $\left(2ab\right)^3=?$

$2xy$

$2x^3y^3$

$8xy$

$8x^3y^3$

Power of a Power: Example

Multiple Choice

Now it is your turn. $\left(t^6\right)^9=?$

$t^{15}$

$t^3$

$t^{-3}$

$t^{\frac{1}{3}}$

$t^{54}$

Multiple Choice

Your turn. What is $\frac{\left(2x\right)^5}{\left(2x\right)^3}=?$

$4x^2$

$8x^2$

$1$

$16x^8$

Simplify the following:

Multiple Choice

Parentheses mean multiplication too....
Simplify:

$\left(4m^2\right)\left(8m^5\right)$

$12m^7$

$32m^7$

$32m^{10}$

$12m^{10}$

Fill in the Blanks

Type answer...

Multiple Choice

Simplify:

$\left(-x^5y^2\right)^4$

$8x^{12}y^6$

256

$x^{20}y^8$

$\frac{1}{256x^8y^{20}}$

Multiple Choice

Mix the properties!! Simplify:

$10m^4\left(2m^3\right)^2$
**PEMDAS always applies**

$40m^{10}$

$20m^{10}$

$20m^9$

$40m^9$

Poll

How well do you understand properties of exponents?

Very well!

I mostly understand the problems.

I still need practice.

Not well!

Multiple Choice

Simplify

$\left(xy^5\right)^2$

$x^2y^{10}$

$x^2y^3$

$xy^3$

$xy^{10}$

Match

Match the following with their simplified answer.

$\frac{x^4}{x^2}$

$x^{-5}$

$\left(\frac{x^3}{x}\right)^{-2}$

$\left(x^{100}\right)^0$

$\left(\frac{1}{x^{-3}}\right)^4$

x²

$\frac{1}{x^5}$

$\frac{1}{x^4}$

x¹²

Poll

My level of understanding

(left to right, NO: I don't get it at all, Whoops: need some help but I'm starting to understand, Nailed It: I can do this on my own.

Show answer

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